Question

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards
are drawn at random and are found to be both clubs. Find the probability of the lost card
being a club.

Answer 1

=50/52 is the answer for the probability of lost card

Answer 2

HEY !!

Answer:

= $\frac{11}{50}$

Step-by-step explanation:

Let A₁ , E₁ an E₂ be the events defined as follows:

A : Cards drawn are both clubs.

E₁ = Lost card is club

E₂ = Lost card is not a club

Then, P (E₁) = $\frac{13}{52} = \frac{1}{4}$

           P (E₂) = $\frac{39}{52} = \frac{3}{4}$

P (A / E₁ ) = Probability of drawing both club cards when lost card is club = 12/51 × 11/50

P (A / E₂) = Probability of drawing both club cards when lost card is club = 13/51 × 12/50

To find : P (E₁ / A)

By Baye's Theorem

     P(E₁ / A)  = P(E₁) P(A/E₁) / P(E₁) P(A/E₁) + P(E₂) P(A/E₂)

        = 1/4 × 12/51 × 11/50 / 1/4 × 12/51 × 11/50 + 3/4 × 13/51 × 12/50

        = 12 × 11 / 12 × 11 + 3 × 13 × 12

        = 11 / 11 + 39

         = $\frac{11}{50}$    FINAL RESULT

GOOD LUCK !!